MethodsofElevationDetermination
Anelevationisaverticaldistanceaboveorbelowa
ghverticaldistancecanbereferenced
toanydatum,insurveying,thereferencedatumthatis
universallyemployedisthatofmeanalevel(MSL).MSLis
assignedaverticalvalue(elevation)of0.000ftor0.000m.
Allotherpointsontheearthcanbedescribedbytheelevations
aboveorbelowzero.
Permanentpointswhoelevationshavebeenprecily
determined(benchmarks)areavailableinmostareasforsurvey
a,7yearsofobrvationsattidalstationsin
Qingdaofrom1950to1956werereducedandadjustedtoprovide
1987,thisdatum
wasfurtherrefinedtoreflectlongperiodicaloceantide
changetoprovideanewnationalverticaldatumof1985,
accordingtotheobrvationsattidalstationsfrom1952to
gh,strictlyspeaking,thenationalverticaldatum
maynotprecilyagreewiththeMSLatspecificpointsonthe
earth’ssurface,thetermMSLisgenerallyudtodescribe
ssignedaverticalvalue(elevation)of0.000
enceinelevationmaybemeasuredbythe
followingmethods:
orspiritleveling,bymeasuringverticaldistances
levelingismostprecimethodofdetermining
elevationsandtheonecommonlyud.
ctortrigonometricleveling,bymeasuringvertical
anglesandhorizontalorslopedistances.
leveling,inwhichverticaldistancesaredetermined
bytacheometryusingengineer’stransitandlevelrod;
plane-tableandalidadeandlevelrod;orlf-reducing
tacheometerandlevelrod.
tricleveling,bymeasuringthedifferencesin
atmosphericpressureatvariousstationsbymeansofa
barometer.
etricleveling,bymeasuringthedifferencesin
gravityatvariousstationsbymeansofagravimeterfor
geodeticpurpos.
alpositioningsystem,inwhichaninertialplatform
hastreemutuallyperpendicularaxes,oneofwhichis“up”,
sothatthesystemyieldlevationasoneofthe
alaccuraciesfrom15to50cmindistancesof
60and100km,respectively,ipment
costixtremelyhighandapplicationsarerestrictedtovery
largeprojectswhereterrain,weather,time,andaccessimpo
specialconstraintsontraditionalmethods.
veyelevationsarereferencedtotheellipsoidbut
canbecorrectedtothedatumifasufficientnumberofpoints
withdatumelevationsarelocatedintheregionsurveyed.
Standarddeviationsinelevationdifferencesof0.053to0.094
marepossibleundertheconditions.
Spiritleveling
Themostprecimethodofdeterminingelevationsandmost
commonlyumethodisdirectlevelingorspiritlevelingwhich
ential
levelingisudtodeterminedifferencesinelevationbetween
pointsthatareremotefromeachotherbyusingasurveyor’
mple,
todeterminetheelevationsofdesiredpointBwithrespectto
apointofknownelevationA(eFigure1),theelevationof
which(BM)isknowntobeabovealevel,thelevelistup
atintermediatepointbetweenAandB,androdreadingsare
e
elevationofthelineofsightoftheinstrument(being
horizontal)isknowntobethelineofsightoftheinstrument
HA+vationofpointBcanbedeterminedbyequation
HB=HA+a-b
InadditiontodeterminingtheelevationofpointB,the
elevationsofanyotherpoints,lowerthanthelineofsight
andvisiblefromthelevel,canbedeterminedinasimilar
calledBacksight(BS)whichisarodreadingtakenonapoint
ofknownelevationinordertoestablishtheelevationofthe
ledForesight(FS)whichis
arodreadingtakenonaturningpoint,benchmark,ortemporary
+arefers
totheHeightofInstrument(HI)whichistheelevationofthe
orefraction,actually
thelineofsightisslightlycurved,theeffectsofcurvature
andrefractionforthehorizontaldistancecanbereducedto
anegligibleamountandnocorrectionforcurvatureand
refractionisnecessaryifbacksightandforesightdistances
arebalancedinpracticaloperation.
TrigonometricLeveling
Trigonometriclevelingisudwheredifficultterrain,such
asmountainousareas,precludestheuofconventional
ernapproachistomeasurethe
slopedistanceandverticalangletothepointinquestion.
Slopedistanceismeasuredusingelectromagneticdistance
measurersandthevertical(orzenith)angleusingatheodolite,
orthetotalstationthatintegratethetwoinstrumentsinto
tationscontainbuilt-in
microprocessorsthatcalculateanddisplaythehorizontal
distancefromthemeasuredslopedistanceandverticalheight.
Thislatterfacilityhasresultedintrigonometricalleveling
beingudforawidevarietyofheightingprocedures,
icconceptoftrigonometrical
asuringthevertical
angleαandthehorizontaldistanceSisud,thenthe
differenceinelevationhABbetweengroundpointsAandBis
therefore:
hAB=S×tanα+i–v
whereiistheverticalheightofthemeasuringcenterofthe
instrumentaboveAandvistheverticalheightofthecenter
ticalanglesarepositivefor
zenithanglesarealwayspositive,butnaturallywhengreater
than90°ometrical
levelingmethodofdeterminingdifferenceinelevationis
limitedtohorizontaldistancelessthan300mwhenmoderate
precisionissufficient,andtoproportionatelyshorter
distancebeyond
300mtheeffectsofcurvatureandrefractionmustbeconsidered
inatetheuncertaintyinthecurvatureand
refractioncorrection,vertical-angleobrvationsaremadeat
bothendsofthelineascloinpointoftimeaspossible.
Thispairofobrvationsistermedreciprocalvertical-angle
rectdifferenceinelevationbetweenthe
twoendsofthelineisthemeanofthetwovaluescomputedboth
wayitherwithorwithouttakingintoaccountcurvatureand
ortantnotesshouldbementionedhereisthat
surveyorsudtoworkingwithspiritlevelshavereferenced
orthometricheights(H)tothe“average”surfaceoftheearth,
r,theelevationcoordinate(h)given
byGPSsolutionsreferstotheheightfromthesurfaceofthe
ellipsoidtothegroundstation.
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